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If you design your site for accessiblity as Krustie stated and for interoperability (cross browser friendliness), you will by default make your site search engine friendly. Most sites depend very heavily on search engine traffic. If you want search engine traffic for your site, you should design your site with search engines in mind. The easiest way to do this is to use real navigational links rather than javascript links and to adhere to W3C (X)HTML and CSS specifications and WCAG (web content accessiblity guidelines).

Now, is there any difference in search engine ranking depending if you used HTML or XHTML

There shouldn't be any difference. Search engines don't care whether you use XHTML or HTML. What they care about is the context of your content and how others preceive your content (e.g. inbound links). The way you use document structure (e.g. H1, H2, P tags, etc.) does matter to a degree.

Now, is there any difference in search engine ranking depending if you used HTML or XHTML

Nope. For the most part, search engines don't even care if you use valid code or not. You still want to use meaningful markup (headings, etc.) and as little code as possible though.

I recommend designing for your users first. I think you'll find that doing that alone will get you very far in terms of designing for search engines, since there's a lot of overlap in the best practices for both areas.

design primarily for users, but always think about making it well seo'ed. As a rule, if you make it easily navigatable for users, it's probably gonna be good for robots as well. Just keep your urls and page titles simple and acurate and have lots of links to your internal pages, and keep your file structure as flat as possible. So it's possible to get to ever page within 3 clicks.